In this article, we have explored multi-item capacitated lot-sizing problem by addressing the backlogging and associated high penalty costs incurred. At the same time, penalty cost for exceeding the resource capacity has also been taken into account. Penalty cost related to both backlogging and overutilizing capacity has been included in main objective function. The main objective is to achieve such a solution that minimizes the total cost. The ingredients of total cost are the setup cost, production cost, inventory holding cost and aforementioned both the penalty costs. To solve this computationally complex problem, a less explored algorithm "biased random key genetic algorithm" has been applied. To the best of our knowledge, this research presents the first application of biased random key genetic algorithm to a lot-sizing problem. To test the effectiveness of proposed algorithm, extensive computational tests are conducted. The encouraging results show that the proposed algorithm is an efficient tool to tackle such complex problems. A comparative study with other existing heuristics shows the supremacy of proposed algorithm in terms of quality of the solution, number of generation and computational time.